The goal of this application is to develop statistical methods for the analysis of failure time data in the presence of missing diagnoses or classification, missing observation time and progression measurement, and missing segments of the target population. These types of missingness are not individual-specific, but rather are characteristic of the entire study population. That is, all subjects are missing a histologically-based diagnosis, or all subjects are missing continuous-valued, continuous-time measurements of progression, or all subjects of a certain type are missing from the study population. These three dimensions of population- wide missingness encompass a broad range of real problems that I have encountered in studies of brain tumors, schwannomas, Multiple Sclerosis (MS), and coronary heart disease (CHD). The brain tumor and schwannoma studies measure several histologic features, with the goal of refining diagnoses to be more prognostic for clinical outcomes. The MS study features a failure endpoint that is defined by a discrete time ordinal longitudinal process. This is common in many cancer studies, which have scored endpoints such as radiologic progression and performance status. The CHD study typifies an emerging common design in which prospective cohorts are sampled mid-study for genetic analysis. This is commonly done to investigate genetic associations with various cancers, as well. An array of statistical methods, including Bayesian and frequentist latent class models, transitional models for ordinal processes, and pseudo likelihood estimation for a biased sample, are used to address these problems. Relevance: This research aims to provide improved statistical methods for the design and analysis of clinical and laboratory studies of cancer. The methods may lead to faster discovery of cancer genes and effective treatments and to better understanding of disease progression through more efficient use of resources.